- A Polynomial Chaos Strategy to Stochastic LQ Optimum Management: Error Bounds and Infinite-Horizon Outcomes(arXiv)
Writer : Ruchuan Ou, Jonas Schießl, Michael Heinrich Baumann, Lars Grüne, Timm Faulwasser
Summary : The stochastic linear-quadratic regulator downside topic to Gaussian disturbances is well-known and normally addressed through a moment-based reformulation. Right here, we leverage polynomial chaos expansions, which mannequin random variables through collection expansions in an appropriate L2 chance house, to sort out the non-Gaussian case. We current the optimum options for finite and infinite horizons. Furthermore, we quantify the truncation error and we analyze the infinite-horizon asymptotics. We present that the restrict of the optimum trajectory is the distinctive resolution to a stationary optimization downside within the sense of chance measures. A numerical instance illustrates our findings
2. Infinite Horizon Imply-Area Linear Quadratic Optimum Management Issues with Jumps and the associated Hamiltonian Programs(arXiv)
Writer : Qingmeng Wei, Yaqi Xu, Zhiyong Yu
Summary : On this work, we deal with an infinite horizon mean-field linear-quadratic stochastic management downside with jumps. Firstly, the infinite horizon linear mean-field stochastic differential equations and backward stochastic differential equations with jumps are studied to help the analysis of the management downside. The worldwide integrability properties of their resolution processes are studied by introducing a form of so-called dissipation circumstances appropriate for the methods involving the mean-field phrases and jumps. For the management downside, we conclude a enough and vital situation of open-loop optimum management by the variational strategy. Apart from, a form of infinite horizon absolutely coupled linear mean-field forward-backward stochastic differential equations with jumps is studied through the use of the tactic of continuation. Such a analysis makes the characterization of the open-loop optimum controls extra simple and full.
